Quiz — 65c6226737679_Corrigé-Devoir de contrôle N°2.pdf

Question 1 sur 10 20:00

[{"id":20809,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. f'(x) = 6x + 2","option_b":"B. f'(x) = 3x + 2","option_c":"C. f'(x) = 6x - 5","option_d":"D. f'(x) = 2x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, (3x²)' = 6x et (2x)' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. f'(x) = 6x + 2\", \"b\": \"B. f'(x) = 3x + 2\", \"c\": \"C. f'(x) = 6x","_debug_options_count":4},{"id":20810,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"A. uₙ = 3 * 2ⁿ","option_b":"B. uₙ = 3 * n²","option_c":"C. uₙ = 2 * 3ⁿ","option_d":"D. uₙ = 3 + 2n","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ. Ici, uₙ = 3 * 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. uₙ = 3 * 2ⁿ\", \"b\": \"B. uₙ = 3 * n²\", \"c\": \"C. uₙ = 2 ","_debug_options_count":4},{"id":20811,"question":"Vrai ou Faux : La dérivée de ln(x) est 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale : la dérivée de ln(x) est bien 1\/x pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":20812,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n - 3) quand n tend vers l'infini ?","option_a":"A. 2","option_b":"B. 0","option_c":"C. 1","option_d":"D. -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 - 3\/n). La limite est donc 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 2\", \"b\": \"B. 0\", \"c\": \"C. 1\", \"d\": \"D. -3\"}}","_debug_options_count":4},{"id":20813,"question":"Vrai ou Faux : Deux événements A et B sont indépendants si P(A ∩ B) = P(A) * P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition de l'indépendance de deux événements en probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":20814,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"A. f'(x) = e^(3x)","option_b":"B. f'(x) = 3e^(3x)","option_c":"C. f'(x) = 3x e^(3x)","option_d":"D. f'(x) = e^(x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 3x, donc u'(x) = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. f'(x) = e^(3x)\", \"b\": \"B. f'(x) = 3e^(3x)\", \"c\": \"C. f'(x) = 3","_debug_options_count":4},{"id":20815,"question":"Une suite arithmétique de premier terme u₀ = 5 et de raison r = -2 a pour terme u₃ :","option_a":"A. u₃ = -1","option_b":"B. u₃ = 1","option_c":"C. u₃ = -3","option_d":"D. u₃ = 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite arithmétique est uₙ = u₀ + n*r. Donc u₃ = 5 + 3*(-2) = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. u₃ = -1\", \"b\": \"B. u₃ = 1\", \"c\": \"C. u₃ = -3\", \"d\": \"D. ","_debug_options_count":4},{"id":20816,"question":"Vrai ou Faux : Si une fonction est dérivable en un point, alors elle est continue en ce point.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental : la dérivabilité implique la continuité.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":20817,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"A. 1\/6","option_b":"B. 1\/3","option_c":"C. 1\/2","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 1\/6\", \"b\": \"B. 1\/3\", \"c\": \"C. 1\/2\", \"d\": \"D. 2\/3\"}}","_debug_options_count":4},{"id":20818,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"A. f'(x) = cos(2x)","option_b":"B. f'(x) = 2cos(2x)","option_c":"C. f'(x) = -2cos(2x)","option_d":"D. f'(x) = sin(2x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de sin(u(x)) est u'(x) * cos(u(x)). Ici, u(x) = 2x, donc u'(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. f'(x) = cos(2x)\", \"b\": \"B. f'(x) = 2cos(2x)\", \"c\": \"C. f'(x) =","_debug_options_count":4}]